It is well-known that the centre of a tree consists of a single vertex or two adjacent vertices. Also, the centre of a tree can be located by an algorithm called leaf-removal [1]}. At the start, leaf-removal removes all the leaves of the input tree \(T\) , and results in a smaller tree \(T_1\) . Next, leaf-removal removes all the leaves of \(T_1\)  and results in \(T_2\) . This process repeats until only a single vertex or two adjacent vertices remain. Then the final remaining vertices are the centre of \(T\) .
